Just unplug your CD player from the system, if it's not too complicated, and connect a headphone amp when you want to use it. If your CD77 is out in the open it should be easy. If the wires are buried, I give up.
As to suggestions for headphones, you just have to listen. I have the Grado GS1000, which are very open sounding, but totally not isolated. You hear everything in the room, so you need quiet. I tried some closed back phones, but they sound too closed-in for me, compared to the Grado. You really need to check it out yourself. Personally, I hate headphones for serious listening enjoyment. Fine for Ipads and stuff, but, for me, not enjoyable at all.
As to suggestions for headphones, you just have to listen. I have the Grado GS1000, which are very open sounding, but totally not isolated. You hear everything in the room, so you need quiet. I tried some closed back phones, but they sound too closed-in for me, compared to the Grado. You really need to check it out yourself. Personally, I hate headphones for serious listening enjoyment. Fine for Ipads and stuff, but, for me, not enjoyable at all.